User-Defined Parameters

Parameter Value Variable
Series Code 21864 ts
Maximum Lag 48 lag.max
Prevision Horizon 12 n.ahead

Getting the Time Series from the BETS database

library(BETS)
data = BETS.get(code)

Information About the Series

info <- BETS.search(code = ts, view = F)
Code Description Periodicity Start Source Unit NA
21864 Physical Production - Intermediate goods Index 2002.1 01/01/2002 feb/2017 IBGE

Graph

## library(mFilter)
trend = fitted(hpfilter(data))

library(dygraphs)
dygraph(cbind(Series = data, Trend = trend), main = info[,"Description"]) %>%
  dyRangeSelector(strokeColor = "gray", fillColor = "gray") %>%
    dyAxis("y", label = info[,"Unit"])

Unit Root Tests

Augmented Dickey-Fuller

  df = BETS.ur_test(y = diff(data), type = "drift", lags = 11, selectlags = "BIC", level = "5pct")
  df$results
##      statistic crit.val rej.H0
## tau2 -3.204720    -2.88    yes
## phi1  5.135789     4.63     no

For a 95% confidence interval, the test statistic tau3 is smaller than the critical value. We therefore conclude that there is no unit root.

Osborn-Chui-Smith-Birchenhall

This test will be performed for lag 12, that is, the frequency of the series 21864.

library(forecast)
s_roots = nsdiffs(data)
print(s_roots)
## [1] 0

According to the OCSB test, there is no seasonal unit root, at least at a 5% significance level.

Auto-Correlation Functions

ACF - Original Series

BETS.corrgram(data, lag.max = lag.max, mode = "bartlett", knit = T)

PACF - Original Series

BETS.corrgram(data, lag.max = lag.max, mode = "simple", type = "partial", knit = T)
  d_ts = data

Model Identification and Estimation

The correlograms from last section gives us enough information to try to identify the underlying SARIMA model parameters. We can confirm our guess by running the auto.arima function from the package forecast. By default, this function uses the AICc (Akaike Information Criterion with Finite Sample Correction) for model selection. Here, we are going to use BIC (Bayesian Information Criterion), in which the penalty term for the number of parameters in the model is larger than in AIC.

model = auto.arima(data, ic = "bic")
summary(model)
## Series: data 
## ARIMA(1,1,0)(1,0,0)[12]                    
## 
## Coefficients:
##           ar1    sar1
##       -0.2362  0.8364
## s.e.   0.0721  0.0353
## 
## sigma^2 estimated as 8.124:  log likelihood=-455.11
## AIC=916.23   AICc=916.36   BIC=925.84
## 
## Training set error measures:
##                        ME     RMSE      MAE         MPE     MAPE     MASE
## Training set -0.005083287 2.826849 2.160359 -0.05500061 2.303063 0.489624
##                    ACF1
## Training set 0.02514418

We see that, according to BIC, the best model is a ARIMA(1,1,0)(1,0,0)[12] .

Forecasts

BETS.predict(model,h=n.ahead, main = info[,"Description"], ylab = info[,"Unit"], knit = T)